Problem: Solve for $x$ and $y$ using elimination. $\begin{align*}4x+8y &= 8 \\ -3x-y &= -6\end{align*}$
Answer: We can eliminate $x$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $3$ and the bottom equation by $4$ $\begin{align*}12x+24y &= 24\\ -12x-4y &= -24\end{align*}$ Add the top and bottom equations. $20y = 0$ Divide both sides by $20$ and reduce as necessary. $y = 0$ Substitute $0$ for $y$ in the top equation. $4x+8( 0) = 8$ $4x = 8$ $4x = 8$ $x = 2$ The solution is $\enspace x = 2, \enspace y = 0$.